Phase shift keying (PSK) is a modulation scheme for transmitting data by changing or modulating, the phase of a reference signal, constituting a carrier wave. PSK uses different phases, commonly two or four, wherein for each a unique pattern of binary bits is assigned. Each bit pattern forms a symbol that is represented by the particular phase. In demodulation, the phase of the received signal is determined and is mapped back to the symbol it represents to recover the original data. Thereby, the phase of the received signal is compared to the unshifted reference signal. This process is called coherent detection.
Alternatively, which is more widely used, non-coherent detection may be used. Here, instead of setting the phase of the wave, data may be modulated onto the carrier wave by changing the phase by a specific amount with respect to a previous phase shift. Therefore, a signal that has been differentially encoded to comprise information may simply be demodulated by detecting the phase between two successively received symbols, i.e. the changes in the phase of the received signal rather than the phase itself are determined. Since this scheme depends on the difference between successive phases, it is termed differential phase shift keying (DPSK).
In non-coherent demodulation or detection, demodulators may thus be used, which operate without knowledge of the absolute value of the phase of the incoming signal reducing the complexity of the system but increasing the probability of error. In detail, once a previous symbol is corrupted, i.e. the previous differential phase shift was distorted e.g. by noise; the error will propagate to the next symbol, since the previous phase is used for the determination of the next symbol. Therefore, it is important to reduce noise in the system to obtain correct symbols.
The carrier wave is usually realized by optical transmission. Here, phase modulated optical transmission may be corrupted by linear and non-linear phase noise which is accumulated along an optical transmission system.
Linear phase noise is caused, for example, by phase variations resulting from added amplified spontaneous emission (ASE) noise of each optical amplifier in a fiber-optic transmission system.
Non-linear phase noise is caused by a non-linear mixing of a signal with the optical amplifier noise owed to the non-linear refractive index of the transmission fibers, known as Kerr effect. It is often referred to as Gordon-Mollenauer noise.
A convenient way to represent PSK schemes is on a constellation diagram showing constellation points in a complex plane (Argand plane) where the real and imaginary axes are termed the in-phase and quadrature axes intersecting each other perpendicularly. The constellation points related to symbols are usually positioned with uniform angular spacing around a circle. For example, in quadrature phase shift keying (QPSK), which uses four different phases, four constellation points are distributed along the circle, preferably so that in each quadrant of the diagram there is one constellation point. In this example, two bits per symbol represented by a constellation point can be encoded.
Both the linear and non-linear phase noise spread signal constellation points, albeit in a different way, and degrade the transmission performance of optical differential phase shift keying (DPSK) and differential quadrature phase shift keying (DQPSK) signals. In other words, the phase relation between successive symbols changes with phase noise, increasing the error rate.
For simplicity, a self-homodyne scheme is often used to demodulate optical phase modulated signals as it eliminates the need for a local phase reference at the receiver, as explained above with respect to DPSK. Such a scheme aggravates, however, the noise impact because a severe corruption of the previous symbol is likely to cause a corruption of the current symbol also, since in this scheme the phase corresponding to the previous symbol constitutes the reference. In the linear regime, self-homodyne reception yields a performance penalty of ˜0.5 dB for DPSK and ˜2 dB for DQPSK signals when compared to ideal homodyne detection, as discussed in patent application, EP 1 694 017 A1.
For mitigation of the linear phase noise and specifically the base line penalty of self-homodyne detection, receivers with electronic compensators based on multi-symbol phase estimation (MSPE) or multiple symbol differential detection (MSDD) have been proposed, for example by H. Leib in “Data-aided noncoherent demodulation of DPSK” IEEE Trans. Commun., Vol. 43, 1995 and U.S. Pat. No. 5,017,883, respectively.
An adaptation of MSPE to optical phase modulated systems with self-homodyne detection can be found, for example, in the papers by X. Liu, “Generalized data-aided multi-symbol phase estimation for improving receiver sensitivity in direct-detection optical m-ary DPSK”, Optics Express, Vol. 15, No. 6, 2007 and “Receiver sensitivity improvement in optical DQPSK and DQPSK/ASK through data-aided multisymbol phase estimation”, Proc. ECOC'06, paper We2.5.6., 2006.
Existing solutions for optical DPSK and DQPSK reception based on MSPE commonly assume that the signal envelope is constant or only slowly varying at the sampling time of the decision device. Whilst this may be true for ideal systems, e.g. a mismatch from the ideal group velocity dispersion at the receiver and non-linear signal interactions on the transmission link can cause intersymbol interference (ISI) and deteriorate the result of the MSPE/MSDD detection process. A modified scheme (here referred to as MSPE-E) takes changes in the signal envelope into account. With moderate additional effort in the electronic domain, this scheme can also be used to detect combined optical DQPSK/amplitude shift keying (ASK) (see the above referenced papers by X. Liu) or quadrature amplitude modulated (QAM) signals.
Non-linear phase noise is mostly dependent on the instantaneous intensity of the optical signal. It can be mitigated by reverting the non-linear phase shift which fluctuations in the light intensity cause on the transmission link (non-linear phase noise compensation, NLPC).
However, existing solutions are expensive and tailored for achieving performance improvements either in the linear regime or in the non-linear regime only, using optical or electronic solutions.